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📅 May 2, 2026 👤 scraface

May 02, 2026

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📌 Let each animation being accepted be a Bernoulli trial with success probability $ p = 0.75 $.

📌 We want the probability that **fewer than two** animations are accepted, i.e., 0 or 1 accepted.

📌 Let $ X \sim \text{Binomial}(3, 0.75) $.

📌 P(X < 2) = P(X = 0) + P(X = 1)

📌 $ P(X = 0) = \binom{3}{0} (0.75)^0 (0.25)^3 = 1 \cdot 1 \cdot 0.015625 = 0.015625 $

📌 $ P(X = 1) = \binom{3}{1} (0.75)^1 (0.25)^2 = 3 \cdot 0.75 \cdot 0.0625 = 0.140625 $

📌 P(X < 2) = 0.015625 + 0.140625 = 0.15625

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